Matakuliah
Tahun
: Manajemen Keuangan 1
: 2009
Ordinary Annuity vs. Annuity Due
Pertemuan 13
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Earlier, we examined this
“ordinary” annuity:
0
1000
1000
1000
1
2
3
Using an interest rate of 8%, we
find that:
• The Future Value (at 3) is
$3,246.40.
• The Present Value (at 0) is
$2,577.10.
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What about this annuity?
1000
1000
1000
0
1
2
3
• Same 3-year time line,
• Same 3 $1000 cash flows, but
• The cash flows occur at the
beginning of each year, rather
than at the end of each year.
• This is an “annuity due.”
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Future Value - annuity due
If you invest $1,000 at the beginning of each of the
next 3 years at 8%, how much would you have at the
end of year 3?
-1000
-1000
0
1
-1000
2
3
Calculator Solution:
Mode = BEGIN
P/Y = 1
I=8
N=3
PMT = -1,000
FV = $3,506.11
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Future Value - annuity due
If you invest $1,000 at the beginning of each of the
next 3 years at 8%, how much would you have at the
end of year 3?
Mathematical Solution:
Simply compound the FV of the
ordinary annuity one more period:
FV = PMT (FVIFA i, n ) (1 + i)
FV = 1,000 (FVIFA .08, 3 ) (1.08)
FV = PMT (1 + i)n - 1
i
(1 + i)
FV = 1,000 (1.08)3 - 1
.08
(1.08)
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(use FVIFA table, or)
= $3,506.11
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Present Value - annuity due
What is the PV of $1,000 at the beginning of each of
the next 3 years, if your opportunity cost is 8%?
1000
1000
1000
0
1
2
3
Calculator Solution:
Mode = BEGIN P/Y = 1
I=8
N=3
PMT = 1,000
PV = $2,783.26
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Present Value - annuity due
Mathematical Solution:
Simply compound the FV of the
ordinary annuity one more period:
PV = PMT (PVIFA i, n ) (1 + i)
PV = 1,000 (PVIFA .08, 3 ) (1.08)
PV = PMT
PV = 1000
1-
1-
1
(1 + i)n
i
1
(1.08 )3
(use PVIFA table, or)
(1 + i)
(1.08)
= $2,783.26
.08
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Annual Percentage Yield (APY)
Which is the better loan:
• 8% compounded annually, or
• 7.85% compounded quarterly?
• We can’t compare these nominal (quoted)
interest rates, because they don’t include the
same number of compounding periods per
year!
We need to calculate the APY.
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Practice Problems
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Retirement Example
If you invest $400 at the end of each month for the
next 30 years at 12%, how much would you have at
the end of year 30?
Mathematical Solution:
FV = PMT (FVIFA i, n )
FV = 400 (FVIFA .01, 360 )
(can’t use FVIFA table)
FV = PMT (1 + i)n - 1
i
FV = 400 (1.01)360 - 1
.01
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= $1,397,985.65
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House Payment Example
If you borrow $100,000 at 7% fixed
interest for 30 years in order to
buy a house, what will be your
monthly house payment?
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House Payment Example
Mathematical Solution:
PV = PMT (PVIFA i, n )
100,000 = PMT (PVIFA .07, 360 )
PV = PMT
(can’t use PVIFA table)
1
1 - (1 + i)n
i
100,000 = PMT 1 -
1
(1.005833 )360
PMT=$665.30
.005833
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